Mixed Causal-Noncausal Autoregressions with Strictly Exogenous Regressors

Alain Hecq, J.V. Issler, Sean Telg

Research output: Working paper / PreprintWorking paper


The mixed autoregressive causal-noncausal model (MAR) has been proposed to estimate economic relationships involving explosive roots in their autoregressive part, as they have stationary forward solutions. In previous work, possible exogenous variables in economic relationships are substituted into the error term to ensure the univariate MAR structure of the variable of interest. To allow for the impact of exogenous fundamental variables directly, we instead consider a MARX representation which allows for the inclusion of strictly exogenous regressors. We develop the asymptotic distribution of the MARX parameters. We assume a Student's t-likelihood to derive closed form solutions of the corresponding standard errors. By means of Monte Carlo simulations, we evaluate the accuracy of MARX model selection based on information criteria. We investigate the influence of the U.S. exchange rate and the U.S. industrial production index on several commodity prices.
Original languageEnglish
PublisherMPRA Paper
Number of pages52
Publication statusPublished - 2017

Publication series

SeriesMunich Personal RePEc Archive

JEL classifications

  • c22 - "Single Equation Models; Single Variables: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models"
  • e31 - "Price Level; Inflation; Deflation"
  • e37 - Prices, Business Fluctuations, and Cycles: Forecasting and Simulation: Models and Applications


  • mixed causal-noncausal process
  • non-Gaussian errors
  • identification
  • rational expectation models
  • commodity prices

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